The Second Law of Thermodynamics in Bioenergetics

Abstract

Bioenergetic processes are viewed as processes of free energy transduction. The free energies of both local equilibrium and fluctuation states are being considered. It is shown that the exchange of thermal energy with the surrounding medium, acting as a reservoir, does not violate the second law of thermodynamics within broad limits. There is sufficient latitude for proteins to carry out their function of transduction utilizing thermal energy in the process.Considerable concern about the relationship of bioenergetic transduction processes and the second law of thermodynamics has been expressed lately (1). It is often difficult to decide whether certain special properties attributed to proteins in these processes violate the second law or not. The difficulty is frequently due to imperfect or ambiguous definitions of the various concepts. It therefore seems necessary to explore the limitations placed on bioenergetic processes by the second law and to demonstrate that enough latitude is left for the proteins to take advantage of thermal energy in carrying out their function. The function in question is the transduction of free energy. This treatment is consequently of a general thermodynamic nature and does not utilize any specific protein model.The time development of bioenergetic systems requires consideration of two kinds of states: (1) Those in which the system spends long times and that represent local thermal equilibria and (2) those in which the system spends short times and that represent thermal fluctuations. A complex bioenergetic process will, in general, consist of an alternating time sequence of sTuch states. The classical formulation of the second law is concerned only with the equilibrium states. The fluctuations are usually considered to belong to statistical mechanics (2) and the results could be derived from it. We shall, however, utilize here a little-known paper by Szilard (3) in which he extended the thermodynamic formulation of the second law to include fluctuations. This will show more dramatically that the fluctuations necessary for proteins to function not only do not contradict the second law, but are a consequence of it.Let us begin with the equilibrium states. The transducing unit is imbedded in a thermal reservoir at temperature T and pressure P and thus its Gibbs potential G = H -TS cannot increase according to the second law (4). Here H is the enthalpy and S is the entropy. Note, however, that if before transduction Gi = H1 -TS, 2655 and afterwards G2 = H2 -TS2, then the second law allows ideally AG = Gi -G2 = 0 and consequently, using analogous definitions of AH and AS, AH -TAS = 0 is allowed. It is, therefore, thermodynamically feasible for a protein to change its enthalpy and entropy in a transduction process by large amounts, if this is done in the above compensatory manner. This does not mean that heat energy is turned into free energy but rather that the transduction of internal energy and heat exchange with the reservoir are part of the same mechanism. The heat may b...

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